Emergence of Calabi-Yau manifolds in high-precision black hole scattering

TL;DR

This paper advances high-precision calculations of black hole scattering by incorporating radiation effects at fifth post-Minkowskian order, revealing Calabi-Yau structures influencing radiated energy and recoil, with implications for gravitational wave physics.

Contribution

It introduces a novel five-loop computation of black hole scattering including radiation, uncovering Calabi-Yau three-fold periods in the process, which was not seen in previous conservative analyses.

Findings

Calabi-Yau three-fold periods contribute to radiated energy and recoil.

The computation employs advanced integration techniques and differential equations.

Comparison with numerical relativity shows good agreement.

Abstract

Using the worldline quantum field theory formalism, we compute the radiation-reacted impulse, scattering angle, radiated energy and recoil of a classical black hole (or neutron star) scattering event at fifth post-Minkowskian and sub-leading self-force orders (5PM-1SF). This state-of-the-art four-loop computation employs advanced integration-by-parts and differential equation technology, and is considerably more challenging than the conservative 5PM-1SF counterpart. As compared with the conservative 5PM-1SF, in the radiation sector Calabi-Yau three-fold periods appear and contribute to the radiated energy and recoil observables. We give an extensive exposition of the canonicalization of the differential equations and provide details on boundary integrations, Feynman rules, and integration-by-parts strategies. Comparisons to numerical relativity are also performed.